5 papers
A high-order, meshless, Lagrangian--Eulerian RBF-FD method for advection--diffusion--reaction on moving manifolds
Matthew Lowery, Grady B. Wright, Varun Shankar
We present a high-order radial basis function-generated finite difference (RBF-FD) method for partial differential equations on moving manifolds o…
Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning
Matthew Lowery, John Turnage, Zachary Morrow +4
This paper introduces the Kernel Neural Operator (KNO), a provably convergent operator-learning architecture that utilizes compositions of deep kernel-based integral operators for…
Fluids You Can Trust: Property-Preserving Operator Learning for Incompressible Flows
Ramansh Sharma, Matthew Lowery, Houman Owhadi +1
We present a novel property-preserving kernel-based operator learning method for incompressible flows governed by the incompressible Navier--Stokes equations. Traditional numerical…
Deep Gaussian Processes for Functional Maps
Matthew Lowery, Zhitong Xu, Da Long +5
Learning mappings between functional spaces, also known as function-on-function regression, is a fundamental problem in functional data analysis with broad applications, including…
An Optimal Weighted Least-Squares Method for Operator Learning
John Turnage, Matthew Lowery, John Jakeman +3
We consider the problem of learning an unknown, possibly nonlinear operator between separable Hilbert spaces from supervised data. Inputs are drawn from a prescribed probability me…